"Y'all are sad for penalizing me for this," she tweeted. "The audacity."
Soon after the tweets, CBS indicated the song was out for good.
In a statement that did not mention Rihanna directly, the network said it would go in a "different direction" and use "our newly created Thursday Night Football theme music".
CBS Sports chairman Sean McManus, speaking last week to Sports Illustrated, said the network had made changes amid criticism that the professional sports world was slow to punish Rice, who was filmed at a casino knocking out the woman who is now his wife.
The network also cut a comedy segment from Thursday's broadcast as "we needed to have the appropriate tone and coverage," the executive told the magazine.
Brown pleaded guilty in 2009 to assaulting Rihanna, who suffered facial injuries and was forced to cancel an appearance at that year's Grammy Awards.
Rihanna later resumed a relationship with Brown, shocking many fans.
- AFP